Heat the oil in a 12-inch sauté pan over medium-high heat until shimmering. Add the onion and carrots and sauté just until they begin to take on color, 3 to 4 minutes.
Add the garlic and stir to combine. Add the meat, salt and pepper, and cook until browned and cooked through, approximately 3 minutes.
Sprinkle the meat with the flour. Toss to coat, and continue to cook for another minute. Add the tomato paste, broth, Worcestershire sauce, and thyme, then stir to combine. Bring to a simmer for 10 to 12 minutes, until the sauce is thickened slightly.
Add the peas to the meat mixture and spread evenly in an ovenproof baking dish. Place on a half sheet pan lined with parchment paper on the middle rack of the oven and bake for 25 minutes, or just until the potatoes begin to brown. Remove to a cooling rack and let rest for at least 15 minutes before serving.